Inductive characterizations of hyperquadrics
Baohua Fu (LMJL)
TL;DR
This paper provides two new characterizations of hyperquadrics, one geometric involving quadric subvarieties and another through secant defect properties of LQEL-manifolds.
Contribution
It introduces two novel characterizations of hyperquadrics, expanding understanding of their geometric and secant defect properties.
Findings
Hyperquadrics are characterized by large-dimensional quadric subvarieties passing through a point.
Hyperquadrics can be described as LQEL-manifolds with significant secant defects.
Abstract
We give two characterizations of hyperquadrics: one as non-degenerate smooth projective varieties swept out by large dimensional quadric subvarieties passing through a point; the other as -manifolds with large secant defects.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds